My personal view is that in the end we are all out on MUP as a part of the comm***ty at large, in that comm***ty we all have to give and take. Yes the parent is responsible for the child, but no single parent is perfect, nor is any cyclist. A small child, jogger with a dog, or even somebody decked out in areo kit on a TT bike can still make a mistake. With that in mind siding with caution in a scenario that could result in injury or property damage we all are responsible to minimize the risk.
So with that I can circle back to my original post. Lets all try to be safe, be courteous, and enjoy our public spaces the best we can. And understand everybody is going to make a mistake or two so be prepared, next time it might just be you...